Basic properties
| Modulus: | \(1309\) | |
| Conductor: | \(1309\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1309.cx
\(\chi_{1309}(9,\cdot)\) \(\chi_{1309}(25,\cdot)\) \(\chi_{1309}(53,\cdot)\) \(\chi_{1309}(60,\cdot)\) \(\chi_{1309}(93,\cdot)\) \(\chi_{1309}(179,\cdot)\) \(\chi_{1309}(212,\cdot)\) \(\chi_{1309}(240,\cdot)\) \(\chi_{1309}(247,\cdot)\) \(\chi_{1309}(291,\cdot)\) \(\chi_{1309}(366,\cdot)\) \(\chi_{1309}(389,\cdot)\) \(\chi_{1309}(410,\cdot)\) \(\chi_{1309}(478,\cdot)\) \(\chi_{1309}(576,\cdot)\) \(\chi_{1309}(597,\cdot)\) \(\chi_{1309}(620,\cdot)\) \(\chi_{1309}(746,\cdot)\) \(\chi_{1309}(774,\cdot)\) \(\chi_{1309}(807,\cdot)\) \(\chi_{1309}(933,\cdot)\) \(\chi_{1309}(961,\cdot)\) \(\chi_{1309}(977,\cdot)\) \(\chi_{1309}(984,\cdot)\) \(\chi_{1309}(1005,\cdot)\) \(\chi_{1309}(1103,\cdot)\) \(\chi_{1309}(1131,\cdot)\) \(\chi_{1309}(1164,\cdot)\) \(\chi_{1309}(1171,\cdot)\) \(\chi_{1309}(1192,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((1123,596,309)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{5}\right),e\left(\frac{1}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 1309 }(247, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{9}{10}\right)\) |